#HashTables #Efficiency #HashingFunction #DataStructure #ComputerScience
Are you puzzled by the efficiency of hash tables even when they are performing extra work using a hashing function? 🤔 Let’s dive into the world of hash tables and hashing functions to understand why they are still considered efficient in computer science.
##Understanding Hash Tables
Hash tables are a type of data structure that store key-value pairs. When you want to store or retrieve a value using a key, hash tables come to the rescue by providing fast lookup times. This is achieved through the use of a hashing function, which converts the key into an index in the hash table where the corresponding value is stored.
###Hashing Function
A hashing function is a crucial component of hash tables that maps keys to indices in the table. The hashing function takes the key as input and produces an output that indicates the location where the value associated with the key should be stored.
####Example:
Let’s consider a simple example where we have a hash table with 10 slots and a hashing function that calculates the modulo of the key to determine the index. If we have a key “25” and the hashing function returns 5, the value associated with the key will be stored at index 5 in the hash table.
##Efficiency of Hash Tables
Hash tables are efficient due to their ability to provide constant-time lookup, insertion, and deletion operations on average. This efficiency is attributed to the following factors:
1. **Constant-Time Operations:** Hash tables offer constant-time operations for retrieving, inserting, and deleting values based on the key. This means that regardless of the size of the hash table, the time complexity of these operations remains O(1) on average.
2. **Collision Handling:** Collisions occur when multiple keys map to the same index in the hash table. Hash tables employ collision resolution techniques such as chaining or open addressing to address collisions and ensure efficient key lookup.
3. **Load Factor:** The load factor of a hash table determines the ratio of the number of keys stored in the table to the total number of slots. By carefully managing the load factor, hash tables can maintain a balance between space efficiency and lookup performance.
##Why Hash Tables are Efficient Despite Extra Work
Now, let’s address the question: Why are hash tables efficient even when they are performing extra work using a hashing function? While hash tables involve additional operations such as calculating the hash value and handling collisions, their efficiency is not compromised for the following reasons:
1. **Optimal Hash Function:** A well-designed hashing function distributes keys evenly across the hash table, minimizing the chances of collisions and ensuring efficient key-value pair retrieval.
2. **Amortized Analysis:** The concept of amortized analysis allows us to evaluate the average time complexity of operations over a series of operations rather than individual cases. In the case of hash tables, the overhead of hashing functions and collision resolution is distributed across multiple operations, leading to efficient overall performance.
3. **Constant-Time Complexity:** Despite the presence of additional operations, the time complexity of hash table operations remains O(1) on average. This constant-time complexity is a key factor in the efficiency of hash tables, even when performing extra work.
In conclusion, hash tables are efficient data structures due to their constant-time operations, effective collision handling, and optimal hash functions. The extra work involved in using a hashing function is offset by the overall efficiency of hash tables in storing and retrieving key-value pairs. So, next time you encounter hash tables in your data processing tasks, rest assured that their efficiency prevails even with the extra work involved. #Efficiency #DataStructure #HashTables
Explore the world of hash tables and hashing functions to harness their efficiency and power in your programming endeavors. Happy hashing! 😄
Because the hash function is constant time.
Big O notation is about scalability, not speed.
So keep in mind that big O doesn’t tell you how fast something is, just how the speed changes as the size of the collection grows. An operation that takes a constant 1 hour is still O(1).
For small tables, it may indeed be faster to do a linear scan of an array rather than hashing the key. But as the size of the table gets bigger, the cost of hashing a single key and jumping directly to the right value remains constant while the cost of scanning and comparing the key against the entire table gets larger.
Well, if you want to be precise, lookups/insertions in hash tables are O(n), but it’s not because of the hashing step. It’s because of how they handle collisions. The *amortized* time complexity is O(1), however.
You know the exact number of extra operations in the hash function, it’s a constant, so it’s O(1). Even if you don’t know the extra number of extra operations, you know that it’s a set number of extra steps in the hash function, so it’s O(1) either way.
The `n` refers to the number of elements that have already been hashed and dealt with. When you insert an element, you hash that element only. It is possible that the hash function is `O(k)` where `k` is the size of the element, but that is kinda separate.
Actually they are O(n) if you count rehashing. The avg time is constant because running what is basically just a modulus is a constant operation.
A % b is not O(n)
It does the hashing function on insertion, and that’s O(1). Of course inserting n elements is O(n), but so is inserting n elements in an array.
Say you have 10 entries, whatever hashing function you do is probably gonna take <10 instructions on insertion compared to the 1 that you’d get with an array. Unless you’re gonna be doing a ton of random access, it makes little sense to use a hashmap here. You pay the initial cost and then it’s marginally faster.
The real value is if you have 1,000,000 entries or some other huge number. In most hashing functions, you’re just doing modulus by 1,000,000 rather than 10, which doesn’t take a significant amount more complexity. Basically, you end up paying the same amount as you did with the 10 entries. And whereas using an array would make you perform 1,000,000 instructions to find the final element, you just need to calculate the hashing function.
TLDR;
Think of it as adjacent to buying instead of renting. You pay an initial/constant cost, and then savings are slowly realized. Not feasible if you plan on moving in a month, but great for if you are planning to settle down (or add 1000000 elements).
Imagine you have a million users. You’re now implementing a “getUserDeets()” function which takes a username and returns info about that user. You need to store the details of the million users somewhere, so let’s compare a couple of options.
First, the hash table. We’ll store a million User objects in a hash table with a key of the username. Finding a user in a hash table works by (a) hashing the input user’s name, (b) jumping to that index in the table, and maybe (c) resolving collisions. c’s unlikely to happen, and b’s basically free, so we just have to pay for the math of hashing, which takes the same amount of time for any input. The performance would be about the same if we had a billion users.
Second, an array. We’ll store a million Users in an array in no particular order. Finding a user in the array works by walking across the entire Array, checking each user’s name against our input, until we get a match. This involves, on average, reading half a million strings. If we grew to a billion users, this algorithm would suddenly take a thousand times as many string comparisons.
If I want to check if an element exists in a normal array, I have to check every position in that array. If I want to check if an element exists in a hash table, all I have to do is run the hash function to figure out where it should be and check that one spot. For really big arrays, the efficiency of checking every spot in the array gets continually worse, but the efficiency of running a hash function always stays the same.
You don’t have to go through potentially the entire array to find the item you’re looking for.
You do it in a single operation, because you essentially know exactly where to look thanks to the key.
If you don’t have the key and hashing function, you’ll have to traverse the entire array (n), or any other number of algorithms depending on the structure of the data, because you don’t know exactly where the desired data is in its structure
Imagine two scenarios
1: array of 100k objects{string key: string value}
2: dictionary<string,string> with 100k
Task: find the item with “key” = abc
In option one to find this item you have to linearly search through 100k items till you find it
In option two you just take the key and do some math to generate the index to search. Perhaps index 18455. So. You go to the memory address for that and check its value. And you’re done. By the time you’ve done the math and checked, the linear search might have only been able to search 200/300 items.
Arrays are faster if you know the index already. If you don’t, and the array is bigger than a few hundred elements, dictionaries will be faster
The upfront math isn’t free, but it doesn’t depend on the number of items. The time to compute the index is the same no matter how many elements are in the dictionary.
A simple example function might be to take the hash of the key and do the modulus of the capacity of the dictionary (capacity is the pre-allocated size similar to how lists work, this can change if the dictionary grows and then everything has to be rehashed but this is not a big deal). And it’s not super expensive.
So if you’re doing lots of searches for anything reasonably big the dictionary will wipe the floor with arrays.